Pledging he would not let voters down, Mr Abbott vowed to govern for all Australians.
"From today I declare that Australia is under new management and open for business," he said. "We will not leave anyone behind."
Victorians punished Labor, with many seats seeing big swings of between 6 and 8 per cent against the party.
The Coalition last night had gained three seats - Deakin and La Trobe, in the eastern suburbs, and Corangamite in the southwest. But, defying predictions of a Labor wipeout, the ALP lost fewer seats than expected - providing some solace to demoralised Labor MPs.
But the Coalition will govern in the 150-seat House of Representatives with a majority of 85 seats or more.
Labor will be reduced to a predicted 54 seats. In a shock result in Queensland, businessman Clive Palmer was expected to secure the seat of Fairfax and Pauline Hanson was still a chance in the Senate in NSW.
Delighted it was not the wipeout predicted he bragged the predictions of his demise were premature.
"I will not be contesting the leadership of the Australian Labor Party," he said.
"I have taken this decision with a heavy heart because I love this movement. But the time has come for renewal. I gave it my all. But it was not enough for us to win. Despite all the prophets of doom we have preserved a viable fighting force for the future."
Former frontbenchers Stephen Smith and Greg Combet urged Mr Rudd to quit politics sparking a by-election.
The Galaxy poll published in News Corp newspapers on Friday provided the most reliable guide to the election outcome of all published polls, predicting a 53-47 two-party-preferred result.